Download maintenance of motor pattern phase relationships in the ventilatory

963
The Journal of Experimental Biology 200, 963–974 (1997)
Printed in Great Britain © The Company of Biologists Limited 1997
JEB0563
MAINTENANCE OF MOTOR PATTERN PHASE RELATIONSHIPS IN THE
VENTILATORY SYSTEM OF THE CRAB
1Neurobiology
R. A. DICAPRIO1,2,*, G. JORDAN2 AND T. HAMPTON2
Program, Department of Biological Sciences and 2College of Osteopathic Medicine, Ohio
University, Athens, OH 45701, USA
Accepted 15 January 1997
Summary
The central pattern generator responsible for the gill
from 470 to 1800 ms over a sevenfold (300–2100 ms) change
ventilation rhythm in the shore crab Carcinus maenas can
in cycle period. Intracellular recordings from ventilatory
produce a functional motor pattern over a large (eightfold)
neurons indicate that there is very little change in the
membrane potential oscillation in the motor neurons with
range of cycle frequencies. One way to continue to generate
a functional motor pattern over such a large frequency
changes in cycle frequency. However, recordings from
range would be to maintain the relative timing (phase) of
nonspiking interneurons in the ventilatory central pattern
the motor pattern as cycle frequency changes. This
generator reveal that the rate of change of the membrane
hypothesis was tested by measuring the phase of eight
potential oscillation of these neurons varies in proportion
events in the motor pattern from extracellular recordings
to changes in cycle frequency. The strict biomechanical
requirements for efficient pumping by the gill bailer, and
at different rhythm frequencies. The motor pattern was
the fact that work is performed in all phases of the motor
found to maintain relatively constant phase relationships
pattern, may require that this motor pattern maintain
among the various motor bursts in this rhythm over a large
phase at all rhythm frequencies.
(sevenfold) range of cycle frequencies, although two phasemaintaining subgroups could be distinguished. Underlying
this phase maintenance is a corresponding change in the
Key words: crab, Carcinus maenas, central pattern generator,
ventilatory rhythm, motor pattern.
time delay between events in the motor pattern ranging
Introduction
In order to maintain functional motor outputs across a wide
range of speeds, the relative timing (phase) of the individual
movements that constitute the output must be appropriately
regulated. Systems that maintain constant time delays between
events in the motor pattern will produce motor outputs in
which phase relationships vary with motor pattern duration,
whereas systems that maintain phase relationships must
increase or decrease the timing between events as the duration
of the motor pattern is altered. This issue has been most
extensively studied in rhythmic motor patterns, and systems
maintaining both constant delay and constant phase have been
observed. For example, in terrestrial locomotion, one portion
of the motor pattern (swing phase) is maintained at a relatively
constant duration over the entire range of walking frequency,
while the phase and duration of the opposing (stance) motor
burst vary as appropriate for a given locomotor frequency
(Grillner, 1981). This relationship, in which return stroke
duration is constant and power stroke duration varies, has also
been observed in insect walking (Pearson and Iles, 1970),
crayfish swimmeret beating (Davis, 1969), insect ventilation
(Miller, 1966) and rhythmic uropod movements in the sand
*e-mail: [email protected].
crab Emerita analoga (Paul, 1971). In other systems such as
Tritonia diomedea swimming (Hume et al. 1982) and the
pyloric rhythm of the lobster stomatogastric system (Hooper,
1993, 1997a,b), motor pattern phasing is relatively constant as
cycle frequency changes. Relatively constant intersegmental
phase relationships are also observed in motor patterns
generated by coupled oscillators such as that for swimming in
the lamprey (Williams, 1992) and leech (Friesen and Pearce,
1993).
Gill ventilation in decapod crustaceans is produced by the
rhythmic dorsoventral movements of the scaphognathite (SG)
or gill bailer of the second maxilla, which pumps water through
the branchial chamber and over the gills. In vivo, the gill bailer
is capable of pumping water at rates from 40 to over
300 cycles min−1 or over an eightfold (0.66–5 Hz) frequency
range (Wilkens, 1976; Mercier and Wilkens, 1984).
In the shore crab Carcinus maenas, the ventilatory motor
pattern is produced by a central pattern generator (CPG;
Delcomyn, 1980) consisting of eight nonspiking interneurons
and 27 motor neurons (DiCaprio and Fourtner, 1984;
DiCaprio, 1989) that drive the five levator and five depressor
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R. A. DICAPRIO, G. JORDAN
AND
T. HAMPTON
muscles of the gill bailer. The levator and depressor groups are
divided into two functional subgroups, Lev1 and Lev2, Dep1
and Dep2, and the normal recruitment sequence of these
muscle groups during forward ventilation is Lev1–Lev2−
Dep1–Dep2 (Young, 1975).
One conclusion of Young’s study of the ventilatory system
was that the motor pattern was essentially phase-constant on
the basis of an analysis of the correlation between cycle period
and time delays in the pattern. However, such correlations are
not a sufficient basis on which to conclude that phase remains
constant in a motor pattern (see Discussion). In addition,
Young’s data were obtained from semi-intact preparations that
preserved the sensory input from the gill bailer and the range
of cycle periods observed was not stated.
In vitro, the frequency of the motor pattern produced by
isolated ganglion preparations could be varied over a sevenfold
range from 0.47 to 3.3 Hz. This large frequency range (cycle
period 2100–300 ms) would require correspondingly large
adjustment of inter-neuronal time delays (up to 1800 ms) to
maintain motor pattern phase. We report here that changes of
this magnitude are, in fact, observed when cycle frequency
varies throughout this range and that the gill ventilation CPG
is capable of producing a relatively phase-constant output over
a sevenfold frequency range.
Materials and methods
Preparation
Male and female green shore crabs, Carcinus maenas (L.),
were used in all experiments. The animals were maintained for
2–10 weeks in artificial seawater aquaria at 10 °C until use. The
isolated ganglion preparation used in this study has been
described in detail elsewhere (Simmers and Bush, 1983;
DiCaprio and Fourtner, 1984). Briefly, the walking legs and
chelae were autotomized and the dorsal carapace, viscera and
brain were removed. The thorax was pinned down in a Sylgardlined dish containing oxygenated crab saline (Ripley et al.
1968). The sternal artery was immediately cannulated and the
thoracic ganglion perfused with oxygenated saline at a rate of
2–3 ml min−1. The nerves to both scaphognathites (SGs) were
dissected from the SG musculature and all remaining nerves
from the thoracic ganglion were severed. The thoracic ganglion
was removed from the thorax and pinned dorsal-surface-up on
the Sylgard base. All experiments were performed at room
temperature (21–22 °C). In experiments where intracellular
recordings were made from ventilatory neurons, the ganglion
was desheathed with fine forceps. The isolated ganglion
preparation used in this study spontaneously expresses the
motor pattern corresponding to forward ventilation for periods
of 6–8 h, with a typical intrinsic frequency of 0.75–1.0 Hz.
Pauses in the ventilatory motor output and spontaneous bouts
of reverse ventilation occurred infrequently in all experiments.
Recording procedures
Extracellular recordings of the ventilatory motor pattern
were made using polyethlyene suction electrodes placed on the
Dep Start
Dep1 End
Lev Start
Lev1 End
Lev End
LEV
DEP
D2a
Dep End
D2a End
D2a Start
500 ms
Fig. 1. Measurement of events in the ventilatory motor pattern. Eight
points in the ventilatory motor pattern can be accurately measured
from extracellular recordings of the motor pattern. With respect to the
four motor neuron groups active during forward ventilation, only the
time of the start of the levator group 2 motor burst could not be
determined from these recordings. The events that can be
unambiguously identified are the start of the entire depressor (DEP)
and levator (LEV) motor group bursts (Dep Start = Dep1 group start;
Lev Start = Lev1 group start), the end point of the depressor group 1
and levator group 1 bursts (Dep1 End and Lev1 End), the end of the
entire depressor and levator bursts (Lev End = Lev2 End; Dep End =
Dep2 end), the start and end of the D2a motor burst (D2a Start and
D2a End) and the start of the depressor group 2 burst (Dep2 Start =
D2a Start).
cut ends of the SG levator (LEV), depressor (DEP) and
depressor muscle D2a motor nerves from either the left or right
side of the ganglion (Fig. 1). A suction electrode was also
placed on the intact circumesophageal connective ipsilateral to
the site of extracellular recording to permit stimulation of
descending fibers that alter the rate of the ventilatory rhythm
(Wilkens et al. 1974). Stimulation of the connective was made
with continuous pulse trains (200 µs duration pulses) at
frequencies of 30–100 Hz. Stimulus amplitude was adjusted to
elicit the maximum change in cycle frequency at the lowest
stimulus frequency and was then held constant as stimulus
frequency was increased to produce a range of ventilatory
cycle frequencies during each experiment. Intracellular
recordings were obtained from neuropilar processes of
ventilatory neurons using glass microelectrodes filled with
2 mol l−1 potassium acetate with resistances in the range
25–30 MΩ. Intracellular voltages were amplified using a
bridge electrometer (WPI 767). All signals were recorded on
an eight-channel instrumentation tape recorder (HP 3968A) for
Phase maintenance in the crab ventilatory system
later analysis and reproduced on an AstroMed MT8800 chart
recorder.
Data analysis
The ventilatory motor pattern consists of alternating bursts
of activity in the motor neurons that innervate the gill bailer.
Levator and depressor activity can each be divided into two
subgroups, levator one and two (Lev1 and Lev2) and depressor
one and two (Dep1 and Dep2), thereby forming a four-phase
motor pattern (Young, 1975). The muscles of the two
subgroups, and hence the motor neurons that drive them, are
activated more or less concurrently during ventilation (Young,
1975), and thus it is impossible to distinguish the activity of
most individual neurons from the four subgroups. However,
the activity of one of the neurons driving a Dep2 group muscle
(D2a) is easily recorded in isolation from a branch of the SG
levator nerve, and this single motor neuron burst was therefore
included in this study.
There are eight points in the ventilatory motor pattern that
can be accurately measured from extracellular recordings of
the motor pattern (Fig. 1). The start of the depressor burst (Dep
Start) was taken as the reference, or zero phase point, in the
cycle and also marks the start of the depressor group one burst.
The next event in the pattern is the start of depressor group
two, indicated by the firing of the D2a motor neuron (D2a
Start). There are two muscles in the depressor two group, D2a
and D2b, and Young’s (1975) electromyographic data
demonstrate that D2a is the first muscle activated in this group.
The onset of D2a motor neuron activity can therefore be used
to determine the Dep2 group start time (Dep2 Start=Dep2a
Start). This is followed by the end of the depressor group one
burst (Dep1 End), the end of the D2a motor neuron burst (D2a
End) and then the end of the D2b motor neuron activity, which
also marks the end of the total depressor burst (Dep End=Dep2
End=Dep2b End). The start of levator group one activity (Lev
Start=Lev1 group start) occurs just before the end of the
depressor burst and is followed by the end of the levator group
one activity (Lev1 End) and the end of the entire levator burst
(Lev End=Lev2 End). Thus, only the time of the start of the
levator group 2 motor burst could not be determined from
extracellular recordings. Measurements of individual events
were always made on the polarity (positive or negative) of the
extracellular recording that provided the most distinct
determination of the transition between bursts. In initial
experiments, measurements were made independently by two
individuals, and no statistical differences were found between
the two data sets.
In each experiment, the slowest cycle frequency occurred in
unstimulated preparations and was in the range 0.75–1.0 Hz.
The circumesophageal connective was stimulated in order to
elicit higher frequencies of the ventilatory motor pattern, and
intervals of relatively constant motor pattern cycle frequency
(variation less than ±5 % of the mean) were selected for
analysis. Time points were measured during these constantfrequency intervals from chart recorder recordings (chart speed
100 mm s−1), using a digital micrometer, for five consecutive
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cycles of the ventilatory pattern. These data were entered into
an Excel spreadsheet (Version 4.0, Microsoft, Inc.) for
calculation of motor pattern phase, average phase and time
delay and for regression analysis. The reference point for all
phase measurements was arbitrarily taken as the start of the
depressor burst, and the phase of other points in the motor
pattern was calculated using the relationship, phase=tev/Tcyc,
where tev is the time from the start of the depressor burst to the
point of interest and Tcyc is the cycle period of the ventilatory
motor output. Data were then transferred to plotting software
(Grapher Version 1.5, Golden Software) for presentation.
Results
Twenty-three experiments were performed and data were
selected for detailed analysis from seven preparations in which
(1) the ventilatory cycle frequency could be varied over at least
a fivefold range, (2) the cycle frequency was relatively stable
during periods of connective stimulation, and (3) all motor
pattern timing points could be clearly identified in the
extracellular recordings.
Phase relationships
Fig. 2 shows a comparison of the ventilatory motor pattern
running at an intrinsic rate of 0.66 Hz (40 cycles min−1) and at
2.36 Hz (142 cycles min−1), or approximately 3.5-fold faster,
during stimulation of the circumesophageal connective (note
the different time scales in the two records). It is apparent from
visual inspection of these two records that the basic structure
and phase relationships of the ventilatory motor pattern are
maintained as the ventilatory rhythm frequency increases. To
confirm this apparent phase constancy, the phase of identifiable
points in the ventilatory motor pattern was plotted using data
from a single preparation (Fig. 3). In this experiment, the
intrinsic (slowest) frequency of the motor pattern was 0.65 Hz
and connective stimulation produced a maximum 4.3-fold
increase of the cycle frequency to 2.8 Hz.
Events in the motor pattern that maintained perfect phase
constancy over this frequency range would produce a
horizontal line (zero slope) with a value equal to the phase
measured at the lowest cycle frequency. The phase of events
that do not compensate for frequency changes, that is, where
the time delay remains constant, would double as frequency
doubles, and hence result in a line with a positive slope. This
is illustrated by the dashed line in Fig. 3, which is a prediction
of the expected phase for D2a Start if this event were to occur
at a constant time delay after the start of the depressor burst.
The slope of this line is tD2a Start/Tcyc, where the delay and cycle
times are measured at the slowest rate of 0.65 Hz. Similar
predictions would result for the other events in the ventilatory
rhythm, except that the slope of each line would increase in
proportion to the (increasing) initial time delays of the other
events in the pattern. The slope of these lines would, therefore,
be greater than that of the line shown for the D2a burst start
time. Note that, for all of these pattern elements, in the absence
of phase compensation, phases greater than 1 (and hence loss
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R. A. DICAPRIO, G. JORDAN
AND
T. HAMPTON
Lev End
1.0
LEV
Lev1 End
0.8
DEP
Dep End
Lev Start
D2a End
Dep1 End
0.6
Phase
D2a
1s
0.4
LEV
D2a Start
0.2
DEP
0
0
D2a
1s
Fig. 2. The ventilatory motor pattern is maintained at different cycle
frequencies. In experiments performed on intact shore crabs (Wilkens,
1976), the ventilation frequencies ranged from 40 beats min−1
(frequency 0.6 Hz, period 1.7 s) to 330 beats min−1 (frequency 5 Hz,
period 0.20 s), an eightfold range. The recordings show the ventilatory
motor output from a typical preparation at its slowest intrinsic
frequency of 40 beats min−1 (0.66 Hz, period 1.5 s) and at a higher
frequency of 142 beats min−1 (2.36 Hz, period 0.42 s) evoked by
connective stimulation. When the time base is scaled proportionally
to the change in frequency (note the different time bars), the motor
patterns appear to be very similar.
of 1:1 cycling with respect to the depressor start) would occur
over the physiologically observed frequency range.
The phase of the levator burst end (Lev End) and the start of
the D2a burst (D2a Start) exhibit the smallest decrease with
cycle frequency (slopes of −0.007 Hz−1 and −0.012 Hz−1
respectively), which result in phase changes of −0.015 and
−0.025 over the 4.3-fold frequency range. The slopes for the
regressions of these data are not significantly different from
zero (P>0.35), indicating that the phase of these events is
constant over this frequency range. All of the other events in
the ventilatory pattern exhibit phase overcompensation as
frequency increases. That is, instead of remaining constant, as
would be expected with perfect phase compensation, or
increasing, as would be expected without compensation, their
phase decreases as rhythm frequency increases. These events
all have a modest phase decrease over the frequency range, with
slopes ranging from −0.024 Hz−1 to −0.054 Hz−1, and all slopes
are significantly different from zero at P<0.04 or better. The
1
2
Cycle frequency (Hz)
3
Fig. 3. The ventilatory motor pattern maintains phase constancy over
a large range of cycle frequencies. The phase of each motor pattern
element is plotted against ventilatory motor pattern frequency. Phase
is calculated by dividing the time delay from the reference point (the
start of the depressor burst) by the cycle period: phase=tev/Tcyc (see
Materials and methods). These data are from a single experiment and
each point is the mean ± S.D. for five cycles of the motor output; solid
lines are the linear regressions for the data. The end of the levator
burst (Lev End) and the start of the D2a burst (D2a Start) keep almost
perfect phase over a 4.3-fold change in frequency, while the phase for
the remaining points in the motor pattern shows a slight
overcompensation as motor pattern frequency increases. The dashed
line is the calculated phase of D2a Start if the time delay were to
remain constant; that is, without phase compensation.
phase of the end of the depressor group 1 motor burst (Dep1
End) has the largest absolute change in phase (−0.13) over the
tested frequency range. In an experiment where intracellular
recordings were obtained from a Lev2 group motor neuron
(data not shown), the phase of the Lev2 Start decreased at
approximately the same rate as the Lev Start phase.
Phase versus cycle frequency data from seven preparations
are presented in Fig. 4, which covers a sevenfold increase in
ventilatory cycle frequencies from 0.5 to 3.4 Hz. These data
illustrate two additional features of phase regulation in the crab
ventilatory system. First, phase for all of the events is
maintained to the same degree in all preparations; that is, the
trends observed in the single experiment presented in Fig. 3
are preserved in the pooled data. For example, the levator burst
ending phase (Lev End) and the depressor D2a motor neuron
starting phase (D2a Start) remain relatively constant (slope
−0.0021 Hz−1 and −0.0091 Hz−1 respectively) over the
Phase maintenance in the crab ventilatory system
Lev End
1.0
0.8
Phase
Lev1 End
0.6
Lev Start
0.4
0.2
0
0
1
2
3
4
1.0
0.8
0.6
Phase
Dep End
0.4
Dep1 End
0.2
0
0
1
2
3
4
1.0
0.8
Phase
0.6
D2a End
0.4
D2a Start
0.2
0
0
1
2
3
Cycle frequency
4
967
Fig. 4. Phase constancy is maintained in all preparations. Data from
seven preparations show that the trends observed in an individual
experiment (Fig. 3) are also seen across different experiments. Each
phase point is an average of five cycles of the motor output selected
for intervals of relatively constant cycle frequency; standard deviation
bars have been omitted for clarity. Phase for the levator burst end (Lev
End) and D2a burst start (D2a Start) is almost constant over a
sevenfold frequency range (0.5–3.4 Hz), whereas overcompensation
is observed for the remaining events in the motor pattern; that is, phase
decreases with increasing frequency. Note that there is very little
difference in the absolute phase value for any of the events from
preparation to preparation.
frequency range, and these slopes are not significantly different
from zero (P>0.57 and P>0.32 respectively). The remaining
events again show a significant and consistent decrease in
phase as the frequency of the motor pattern increases (range of
slopes −0.048 Hz−1 to −0.068 Hz−1; P<0.0l for all), indicating
a phase overcompensation as frequency increases. The largest
phase shift was again seen for the Dep1 motor burst ending
(Dep1 End), with a total phase change of −0.12 over the entire
frequency range. Second, the low scatter of the experimental
points around the regression lines demonstrates that, at any
given frequency, the phase of all events is very similar from
preparation to preparation. This system thus not only maintains
phase in a consistent manner from animal to animal, but the
timing of the motor pattern is the same for all animals.
Burst durations and duty cycle
The phase measurements also provide a description of the
relative burst durations (duty cycle) for each motor neuron
group in the ventilatory pattern. If the regression lines for the
starting and ending phases of any given motor burst are
parallel, duty cycle (burst duration/cycle period) would remain
constant; that is, the burst would occupy a constant percentage
of the cycle period at any cycle frequency. For example, the
starting and ending phases of the levator group one burst
(Lev1) both decrease at similar rates (slopes −0.048 Hz−1 and
−0.052 Hz−1) as frequency increases, and therefore the Lev1
burst duration maintains a relatively constant duty cycle. Motor
neuron bursts whose starting and ending phase lines are not
parallel do not maintain a constant duty cycle; divergence of
these lines indicates an increasing duty cycle with increasing
frequency, while converging lines indicate a decreasing duty
cycle as frequency increases. The regression lines for the start
(D2a Start) and end (Dep End) of the Dep2 burst in Fig. 4, for
example, converge as frequency increases (slope −0.009 Hz−1
and −0.056 Hz−1 respectively), and hence the duty cycle of the
Dep2 group decreases as cycle frequency increases. In contrast,
the regression lines for the start (Lev Start) and end (Lev End)
of the total levator burst diverge (slopes of −0.047 Hz−1 and
−0.002 Hz−1 respectively), indicating an increase in duty cycle
with increasing frequency.
The duty cycles for the five motor bursts that can be
distinguished in extracellular recordings are shown in Fig. 5 as
a function of cycle frequency. The duty cycle for each of the
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R. A. DICAPRIO, G. JORDAN
AND
T. HAMPTON
A
0.8
T0
Dep
T0
A
B
0.6
C
Dep1
Dep2
Duty cycle
tB
tC
Lev
T0/2
A
0.4
B
C
Lev1
B
0
0
1
2
Cycle frequency (Hz)
3
4
Fig. 5. Changes in the duty cycle of the motor bursts with cycle
frequency. At the lowest cycle frequency that the ventilatory central
pattern generator will generate, the complete depressor burst has a
duty cycle of approximately 0.73 while the levator burst has a duty
cycle of approximately 0.37. With increasing frequency, the duty
cycles of the depressor burst (Dep) and the two subsets for the
depressor activity, the depressor group 1 bursts (Dep1) and the
depressor group 2 bursts (Dep2), all decrease, with slopes of
−0.059 Hz−1 for Dep, −0.068 Hz−1 for Dep1 and −0.047 Hz−1 for
Dep2. The duty cycle for the levator group 1 burst (Lev1) remains
constant (slope −0.00094 Hz−1; P>0.9) at all cycle frequencies, while
the duty cycle of the total levator burst (Lev) increases with increasing
frequency with a slope of 0.046 Hz−1.
depressor groups and the overall depressor burst (Dep Start to
Dep End) decreases as frequency increases. As already noted,
the Lev1 group maintains a constant duty cycle, although the
overall duty cycle of total levator activity (Lev Start to Lev
End) increases as frequency increases. It was not possible to
determine the duty cycle for the Lev2 burst, as the Lev2 start
time cannot be determined accurately from extracellular
recordings. At low cycle frequencies, the depressor burst
occupies a larger percentage of the ventilatory cycle than the
levator burst (70 % versus 35 %) with an overlap of
approximately 5 % of the cycle period. The decrease in
depressor burst duty cycle and concurrent increase in levator
burst duty cycle with increasing frequency result in the duty
cycle of the levator and depressor bursts both approaching 0.55
at the highest cycle frequency.
Time delays in the motor pattern
To appreciate fully the task that the ventilatory CPG must
perform to maintain phase constancy, it is useful to consider a
hypothetical example (Fig. 6). In the three-phase motor pattern
shown here (Fig. 6A), neuron A defines the cycle period and is
Time delay
0.2
C
2
B
1
1
2
Cycle period
3
Fig. 6. Phase constancy requires proportional changes in the time
delay as cycle period changes. (A) In order to maintain phase
constancy in the three-phase motor pattern shown here, the time delay
from the reference point (beginning of the burst in neuron A) must
decrease in proportion to the decrease in cycle period. The arrowheads
denote the expected time of occurrence of the bursts in neurons B and
C if the time delays did not change as cycle period changed. Perfect
phase constancy will result when the time delay to the event of interest
(e.g. the beginning of the burst in neuron B) changes to t=(t0/T0)T,
where t is the calculated delay required for perfect phase, t0 and T0
are the time delay and cycle period at the slowest rate, respectively,
and T is the new cycle period. The unfilled bursts in the record for
neuron B indicate an instance where the time delay for this neuron
decreases with the decrease in cycle period, but by an amount less
than that required for perfect phase maintenance. (B) The broken line
on the graph is the relationship between time delay and period that
results in this particular case. The solid lines are for the case where
there is perfect phase maintenance. Note that the slope (t0/T0) of the
perfect phase line is determined by the time delay at the longest cycle
period, and therefore the slope of the perfect phase line for neuron C
is greater than the slope of the perfect phase line for neuron B.
assumed to be a pacemaker cell that keeps a constant duty cycle
as the period of the rhythm is altered. Neurons B and C fire in
bursts after neuron A, but with different initial time delays after
the start of the burst in neuron A. When the period of this rhythm
is decreased to half of its initial value (a doubling of cycle
frequency), to maintain phase constancy, the time delay from the
reference point in the motor pattern (the start of the burst in A)
must also decrease by half. This constraint also results in a
proportional decrease in the duration of each burst period in the
Phase maintenance in the crab ventilatory system
1.6
1.2
Lev End
Lev1 End
Lev Start
Dep End
D2a End
Dep1 End
D2a Start
1.2
Time delay (s)
969
0.8
0.8
0.4
0.4
0
0
0.4
0.8
1.2
0
1.6
0
Cycle period (s)
0.4
0.8
1.2
1.6
Fig. 7. Large changes in time delays are required to maintain phase constancy in the ventilatory motor pattern. Time delays for each of the
readily identifiable points in the ventilatory motor pattern are plotted with respect to cycle period. Data from a single experimental preparation
(same as that shown in Fig. 3) that produced a fourfold increase in cycle frequency. Linear regressions (solid lines) for the data show that the
measured changes in time delay are close to the ideal time delay required for maintenance of perfect phase. The ideal slopes were calculated
from the average time delay and period during five cycles of the slowest (unstimulated) ventilatory rhythm. Note that the smallest change in
time delay is for the D2a burst start time (D2a Start), which decreases by 240 ms, while the delay to the levator burst end (Lev End) decreases
by 1220 ms over the range of cycle periods (365–1570 ms) observed in this preparation. The dashed lines indicate the calculated change in time
delay required for each event in order to maintain a constant phase as cycle period changes.
pattern as the cycle period decreases and, therefore, in a constant
duty cycle for the motor bursts. Note that changing cycle period
without phase compensation would disrupt the motor pattern.
For instance, a decrease in the cycle period without concurrent
changes in time delay would place the beginning of the burst in
neuron B much later in the cycle, and the beginning of the burst
in neuron C would fall outside the cycle period (the
uncompensated positions for the start of these bursts are
indicated by the arrowheads). The time delay, tev, required for
perfect phase constancy for each neuron in the pattern is given
by tev=(t0/T0)T, where t0 and T0 are the time delay and cycle
period at the lowest (intrinsic) cycle frequency, respectively, and
T is the new cycle period. Note that the slope (t0/T0) of this
relationship is different for each neuron in the pattern, with the
slope increasing as the initial time delay (and hence initial phase)
from the reference point increases, but the y-intercept is zero in
all cases (Fig. 6B). The slope of this relationship for an event
that does not maintain perfect phase will not equal t0/T0, and the
y-intercept will not be equal to zero; a slope of less than t0/T0
and a positive intercept denote an event that increases in phase
as period decreases, while a slope greater than t0/T0 and a
negative intercept indicate that the phase decreases with
decreasing cycle period. The unfilled bursts for neuron B in
Fig. 6A are examples of an instance where this neuron does not
keep perfect phase, although the time delay does decrease with
decreasing cycle period and there is a strong correlation between
burst delay and cycle period (broken line, Fig. 6B).
The relatively constant phase versus cycle frequency
relationships observed in the ventilatory system therefore
indicate that large proportional changes in the time delays of
each event occur as cycle period changes. Fig. 7 shows these
time delays in the motor pattern as the ventilatory cycle period
changes in a single experiment (these data are from the
preparation shown in Fig. 3). Cycle period and time delay are
highly correlated for all of the measured events in the
ventilatory motor pattern. The correlation coefficients of the
linear regressions (solid lines) to the data are all greater than
0.99 except for the D2a start delay, where r=0.945, and all
slopes are significantly different from zero at P<0.04 or better.
More importantly with respect to phase maintenance, the
differences between the slope of the regression and the slope
of the line calculated for perfect phase maintenance (dashed
lines) are extremely small. This close agreement between
experimental and predicted results is expected given the
modest changes in phase for each event seen in Fig. 3. The
smallest time delay change is seen in the D2a burst start time,
which decreases by 240 ms, whereas perfect phase
maintenance would require a decrease of 225 ms. The time
delay to the end of the levator burst decreases by the largest
amount, 1220 ms, as this event has the longest initial delay
from the start of the depressor burst, while a decrease of
1225 ms would be required in order to maintain perfect phase.
The difference between ideal and measured time delays is very
small for these two events, as they maintain the most constant
970
R. A. DICAPRIO, G. JORDAN
AND
T. HAMPTON
2.5
2.0
Lev End
Lev1 End
Lev Start
Time delay (s)
2.0
1.6
1.5
1.2
1.0
0.8
0.5
0.4
0
0
0
0.5
1.0
1.5
2.0
2.5
0
Cycle period (s)
Dep End
D2a End
D1 End
D2a Start
0.5
1.0
1.5
2.0
2.5
Fig. 8. Time delays for pooled experimental data from seven experiments spanning a sevenfold range of cycle frequency. The time delay changes
observed in the single experiment presented in Fig. 7 are maintained when data from multiple preparations are combined. The variation in time
delay is highly correlated with cycle period (r>0.93 for all) over the range 300–1200 ms. The time delay to D2a Start requires the smallest
change with cycle period (470 ms) as this is the first event after the start of the depressor burst which was used as the motor pattern reference
point. The largest change in time delay (1800 ms) occurs for the time to the end of the levator burst, Lev End.
phase (see Fig. 4). Note that, even for the event that has the
largest deviation from constant phase (Dep1 End), the
difference between the ideal time delay for constant phase at
the smallest cycle period (182 ms) and the actual time delay
(136 ms) is still rather small and is only 7 % of the total (ideal)
change in time delay required for this event.
Pooled data from the same seven experiments shown in
Fig. 4 are presented in Fig. 8. Again, the slopes of the time
delay versus cycle period relationships are significantly
different from zero (P<0.001) and highly correlated: all the
correlation coefficients are greater than 0.99 except for the D2a
start delay, where r=0.93. Over the larger range of cycle
periods shown for the pooled data (300–2100 ms), the
magnitudes of the time delay changes required for phase
maintenance are also increased. The delay for the D2a start
time decreases by 470 ms from the longest to the shortest
period observed, while the delay to the end of the levator burst
decreases by approximately 1800 ms over the same range of
cycle periods.
Intracellular correlates of phase maintenance
The mechanisms that maintain phase relationships in the
ventilatory CPG output must reside in the network interactions
of the CPG and/or the intrinsic membrane properties of the
neurons that constitute this CPG. Unfortunately, we do not
possess a detailed circuit for the ventilatory CPG or sufficient
data regarding the membrane properties of most of the
ventilatory neurons to allow a definitive determination of the
mechanisms that underlie phase maintenance in this system.
However, inspection of intracellular recordings from
ventilatory motor neurons and interneurons does give some
insight into the possible location of these mechanisms. Fig. 9
presents intracellular recordings from two motor neurons and
two nonspiking interneurons in the ventilatory CPG at different
cycle frequencies. The motor neurons that drive the ventilatory
muscle have been found to exhibit plateau properties when the
CPG is active (DiCaprio, 1993). Fig. 9A is an intracellular
recording from a Dep1 group motor neuron at four different
cycle periods (0.9, 0.76, 0.54 and 0.44 s) with the traces aligned
at the beginning of the burst. There is no difference in the initial
slope of the depolarizing phase of the membrane potential
oscillation in this neuron, although there is a slight, but
significant, change in slope (P<0.03) during the
hyperpolarizing phase, with the slope decreasing as cycle
period increases. The underlying membrane potential
oscillation of a Lev1 motor neuron (Fig. 9B) at four different
cycle periods (1.5, 1.25, 1.16 and 0.88 s) is also essentially
constant as the period of the rhythm decreases. In both cases,
the voltage threshold for spike initiation in the neurons remains
constant during changes in cycle period. These recordings
indicate that the motor neurons function as bistable elements
in that the kinetics of their plateau potential transitions are
constant as cycle frequency changes and, hence, changes in
their membrane properties are unlikely to play a major role in
motor pattern phase maintenance.
The ventilatory interneurons, however, exhibit much larger
changes in their membrane potential trajectories as cycle
frequency changes. Fig. 9C,D presents intracellular recordings
from interneuron CPGi6 at four different cycle periods (1.65,
1.25, 1.05 and 0.96 s) and interneuron CPGi8 at three cycle
periods (1.56, 1.0 and 0.64 s) that are aligned on the
hyperpolarizing phase of their membrane potential oscillation.
Phase maintenance in the crab ventilatory system
971
Fig. 9. Intracellular recordings from ventilatory
A
B
motor neurons and interneurons as ventilatory cycle
period changes. A Dep1 group motor neuron (A) is
shown at four different cycle periods (0.9, 0.76, 0.54
and 0.44 s) and a Lev1 motor neuron (B) at four
different cycle periods (1.5, 1.25, 1.16 and 0.88 s).
Dep1 motor neuron
500 ms
Lev1 motor neuron
1s
The membrane potential oscillations of these motor
neurons exhibit very little variability as cycle period
decreases. Note, however, that the slope of the
C
repolarizing phase of the Dep1 motor neuron
decreases as cycle period increases. Intracellular
3
2
recordings from nonspiking interneurons CPGi6 (C)
at cycle periods of 1.65, 1.25, 1.05 and 0.96 s are
1
aligned on the hyperpolarizing phase of the
membrane potential oscillation. Interneuron CPGi8
Interneuron CPGi6
500 ms
(D) is shown at three cycle periods 1.56, 1.0 and
0.64 s, again aligned on the hyperpolarizing phase of
the membrane potential oscillation. Both interneurons
D
have almost uniform membrane potential trajectories
during the hyperpolarizing phase of their oscillation,
but the slope of the depolarizing phase decreases in
proportion to the increase in cycle period. The scaling
of membrane potential trajectory with cycle period is
Interneuron CPGi8
1s
demonstrated to the right of each record, where a
recording at the shortest cycle period is superimposed on a recording at the longest cycle period after it had been graphically stretched (1.7×
for CPGi6 and 2.4× for CPGi8) to fit the longer cycle period. The numbers adjacent to the record of CPGi6 refer to the three different rates of
change in the membrane potential observed as this neuron depolarizes.
Both interneurons have almost uniform membrane potential
trajectories during the hyperpolarizing phase of their oscillation,
but the slope of the depolarizing phase increases in proportion
to the increase in cycle frequency. The depolarizing phase of
the membrane potential oscillation in interneuron CPGi6 has
several inflection points before the neuron reaches its maximum
depolarized level. The slopes of the first two depolarizations
(Fig. 9C, regions 1 and 2) are correlated (r>0.9) with cycle
frequency and the change in slope is significant (P<0.05), while
the slopes of the final depolarizing phase (Fig. 9C, region 3) are
not significantly different (P>0.63). The depolarizing phase of
the membrane potential oscillation of CPGi8 also has at least
two inflection points, but these are rather difficult to discern as
the cycle frequency increases. If the slope of the depolarization
is measured from the point where the cell starts to depolarize
to the point of maximum depolarization, the slopes are
correlated (r=0.99) with cycle frequency and the change in
slope is significant (P<0.01). As has been noted previously with
respect to changes in time delay, the mere correlation between
these slopes and cycle frequency does not provide evidence that
these parameters are changing in exact proportion to the change
in cycle frequency.
To determine whether the membrane potential oscillation of
the interneurons is scaled with respect to cycle frequency, the
membrane potential waveforms are compared at two different
cycle frequencies after adjusting the time scale of the higherfrequency oscillation (right-hand panels of Fig. 9C,D). One
oscillation cycle at the highest cycle frequency has been
superimposed over one cycle at the lowest frequency after the
high-frequency record has been graphically stretched (1.7× for
CPGi6 and 2.4× for CPGi8) to match the cycle period at the
lower frequency. The membrane potential oscillations and their
amplitudes are extremely similar when scaled to the same time
base. It would therefore appear that the membrane potential
trajectory of these interneurons changes in almost exact
proportion to the change in cycle frequency, which is
consistent with the hypothesis that the changes in motor pattern
timing occur at the level of the interneurons.
Discussion
In Young’s (1975) comprehensive description of the
ventilatory musculature and motor pattern in Carcinus
maenas, he stated that the motor pattern was phase-constant.
This conclusion was based on the observed strong positive
correlation of both burst latency (time delay) and burst
duration with ventilatory cycle period. However, a correlation
between time delay and cycle period does not provide
sufficient data to conclude that phase is constant in a motor
pattern. Such phase constancy requires that time delays
change in exact proportion to the change in cycle period rather
than simply correlate with period. For example, if the cycle
period (T0) of a motor pattern decreases to half of its initial
value (0.5T0), and all of the time delays (t0) decrease by the
same factor (0.5 t0), then:
phase = t0/T0 = 0.5t0/0.5T0 ,
(1)
will remain constant. If, however, latencies change by a
different factor (e.g. 0.7), the slope of the time delay versus
cycle period relationship:
972
R. A. DICAPRIO, G. JORDAN
AND
T. HAMPTON
slope = (t0 − 0.7t0)/(T0 − 0.5T0) = 0.3t0/0.5T0 = 0.6(t0/T0) , (2)
will be different from the value required for perfect phase
maintenance (slope = t0/T0 = initial phase at the longest cycle
period, T0) and the y-intercept will not be equal to zero. The
time delays for such events will still be perfectly correlated
with cycle period, but the phase of each event in the pattern
will vary as period changes (see Fig. 6). Likewise, a perfect
correlation between burst duration and cycle period will exist
when a motor pattern is phase-constant, but such a correlation
does not, in and of itself, denote phase constancy. For example,
if cycle period changes by a factor of 0.5, but the time delay
for the starting time of a burst changes by a different factor,
burst duration will still correlate with cycle period, but the
(starting) phase of the burst will shift with the change in period.
Young’s analysis only used correlation, rather than the direct
determination of phase that is required in order to demonstrate
phase constancy and, as such, does not demonstrate that the
ventilatory motor pattern is phase-constant.
The data presented here demonstrate that the isolated
ventilatory CPG of the shore crab maintains a high degree of
phase constancy over a large range of cycle frequencies. Phase
measurements using pooled experimental data show that the
phase of two of the events in the pattern, Lev End and D2a Start,
remains constant over a sevenfold increase in cycle frequency,
with changes of only −0.0021 Hz−1 and −0.0091 Hz−1,
respectively, and these slopes are not significantly different
from zero. The remaining five points in the motor pattern that
were examined exhibit a decrease in phase (slopes range from
−0.052 Hz−1 to −0.068 Hz−1; P<0.01) over the same frequency
range and are therefore overcompensated for changes in cycle
frequency. These results are consistent from preparation to
preparation, as shown by the relatively small scatter of the
points around the regression line. Furthermore, the phase of any
of the measured events at any given cycle frequency is
approximately the same in all experiments. This motor pattern
is therefore extremely similar in all animals; that is, there is very
little animal-specific variation in phase, in contrast to the data
obtained in other systems (Hooper, 1997a,b).
Two subgroups can be distinguished within the motor pattern
with respect to phase maintenance. First, Dep1 Start, Lev End
and D2a Start phases remain essentially constant with respect
to each other as cycle frequency increases. These three events
therefore constitute a phase-maintaining subgroup within the
ventilatory motor pattern. Second, the phase of the remaining
events, Lev Start, Lev1 End, Dep End, Dep1 End and D2a End,
all decrease with respect to the Dep Start reference as cycle
frequency increases. Given the similar slopes of the phase
versus frequency relationship for these five events (range
−0.068 Hz−1 to −0.048 Hz−1), they therefore constitute another
phase-maintaining subgroup. Limited intracellular recordings
from Lev2 group motor neurons indicate that the start of this
burst may also maintain phase within the second subgroup.
Time delay, duty cycle and motor pattern
The relatively constant phase relationships observed in the
ventilatory motor pattern result from a change in the time delay
of each of the events in the motor pattern as the cycle period
of the rhythm varies. As expected, the time delay change for
each measured event is very close to the value needed for
perfect phase maintenance (Figs 7, 8). Given the sevenfold
range of cycle period (300–2100 ms) observed in these
experiments, the maximum changes in time delay are quite
large, ranging from 470 ms for the D2a start time to 1800 ms
for the levator burst end time. Although the deviations from
the changes in time delay required for perfect phase
maintenance are small in the context of the large changes that
are observed, the effect of this difference becomes more
pronounced with respect to motor pattern phase as the
deviation from ideal delay becomes a larger percentage of the
cycle period as frequency increases.
The segregation of the start and end times of the various
motor bursts into different phase-maintaining subgroups
results in the duty cycle of all but the levator group 1 burst
varying with cycle frequency. At low cycle frequencies
(approximately 0.6 Hz) the total depressor burst occupies
approximately 75 % of the cycle period while the total levator
burst lasts for approximately 35 % of the cycle, with a 5 %
overlap. As cycle frequency increases, levator duty cycle
increases and depressor duty cycle decreases while the overlap
remains relatively constant, resulting in approximately equal
duty cycles for the levators and depressors at high cycle
frequencies (approximately 3.5 Hz). The significance of these
changes in duty cycle are impossible to assess without a more
thorough understanding of the biomechanics and
hydrodynamics of the ventilatory pump.
Changes in relative timing in a motor pattern may be caused
by changes in the strength of synaptic excitation or inhibition
to neurons in a CPG or by changes in the intrinsic membrane
properties of the neurons in the network. For example, Eisen
and Marder (1984) demonstrated in the pyloric motor pattern
of the lobster stomatogastric system, that PY motor neuron
firing could be phase-advanced or phase-retarded by changes
in the burst amplitude of the presynaptic PD neurons, which
provide chemically mediated synaptic inhibition of the PY
neuron. Changes in phase relationships can also be caused by
altering the strength of electrical synaptic coupling between
pairs of neurons (Sharp et al. 1992) or, in a model system with
both electrical and chemical synaptic interactions, by varying
the relative strength of the two synapses (Mulloney et al.
1981).
Alternatively, intrinsic membrane properties such as postinhibitory rebound and plateau potentials can also cause
changes in time delays in rhythmic motor patterns. Hooper
(1993, 1994) has shown that changing either the amplitude or
the temporal characteristics of rhythmic hyperpolarizing
current injections can alter rebound firing delays in neurons of
the pyloric system. Neuromodulators can also effect phase
changes by modifying intrinsic membrane properties.
Dopamine, for example, causes an increase in the rate of postinhibitory rebound, and therefore a phase advance of the PY
neuron in the pyloric motor pattern, by decreasing the
Phase maintenance in the crab ventilatory system
amplitude of the transient potassium current IA (HarrisWarrick et al. 1995a). In this system, dopamine can also phaseadvance the LP neuron by reducing IA and by shifting the
voltage-dependence of the hyperpolarization-activated inward
current Ih (Harris-Warrick et al. 1995b).
Intracellular correlates of phase maintenance
It is difficult to speculate on the mechanisms that underlie
the changes in time delays and the resultant phase
compensation observed in this system, because of a lack of
detailed information about the intrinsic cellular and/or synaptic
properties of the neurons in the ventilatory CPG. However, it
does not appear that the plateau properties (DiCaprio, 1993) of
the motor neurons play a large role in these changes, as the
transition time between their hyperpolarized and depolarized
states does not change with cycle frequency. The timing of the
motor neuron bursts is presumably determined instead by the
timing of the excitatory and inhibitory inputs that they receive
from the nonspiking interneurons in the CPG.
In contrast, the rate of change of membrane potential in these
interneurons does change with cycle frequency, and these
changes are proportional to the change in frequency. Although
similar data are not available for all eight CPG interneurons,
especially over the large frequency range used in this study,
the limited data are consistent with the hypothesis that the
interneurons are the principal determinants of phase
compensation in this system. These changes are presumably
due to the kinetics of the intrinsic membrane properties of these
neurons, but insufficient information about the conductances
present in these neurons is available to allow speculation about
the role of these properties in phase regulation.
Given that the interneurons in the ventilatory CPG are all
nonspiking (DiCaprio, 1989), it is difficult to determine the
phase of these cells in the motor pattern without a knowledge
of transmitter release thresholds for each neuron. In fact, the
depolarizing phase of the membrane potential oscillation of
these neurons typically overlaps the start and end times of
different events, or different groups, in the motor pattern and
therefore cannot be simply associated with discrete motor
bursts. For example, the depolarized phase of interneuron
CPGi6 (Fig. 9C) occurs near the end of the depressor burst and
continues until the end of the Lev1 group burst; CPGi8 remains
relatively depolarized during the entire levator burst.
However, the frequency-dependent change in slope of the
membrane potential trajectories results in an increase in the
amount of time that these interneurons spend in transition from
their minimum to maximum membrane potentials. As the
typical maximum hyperpolarized level of the nonspiking
interneurons is in the range −60 to −50 mV, with peak-to-peak
amplitude ranging from 15 to 45 mV, the interneurons may be
subthreshold for transmitter release for a longer time as cycle
period increases. Effective synaptic input to other interneurons
will, therefore, be delayed in addition to the delay of any inputs
that trigger or terminate the plateau-potential-mediated bursts
in the motor neurons. In the event that these interneurons are
continuously releasing transmitter or interact via electrical
973
synapses, the change in the slope of the membrane potential of
these neurons could still serve to alter the timing of the
interactions between neurons in the CPG on the basis of their
graded interactions.
Necessity for phase compensation in gill ventilation
Maintenance of motor pattern phase during changes in the
ventilatory cycle period is required to preserve the relative
timing of motor activity and to ensure that individual
components of the pattern are expressed during each cycle. The
ventilatory motor pattern not only satisfies this minimum
requirement, but the phase of the two events is essentially
constant as cycle period changes. In addition, although the
phase of the remaining events in the pattern does change
(decrease) with cycle period, these changes reflect an
overcompensation for the change in cycle period. In contrast
to various locomotor systems where the return stroke phase in
the motor pattern remains relatively constant, the ventilatory
CPG does work during both the levation and depression
portions of the cycle. Phase constancy may therefore be a
functional requirement of the crab ventilatory system because
of the biomechanical constraints of the SG pumping action.
The anterior and posterior tips of the SG spend most of the
ventilatory cycle in their maximum levated or depressed
position, with fast coordinated antiphase transitions between
the two extremes of movement (Young, 1975). The transition
period for each of these movements lasts for approximately
10 % of the total ventilatory cycle, and the transitions occur at
the Lev End to Dep Start phase and the Dep End to Lev Start
phase. Note that the relative phase of the Lev End to Dep Start
transition is constant with increasing cycle frequency, and the
relative phase between Dep End and Lev Start only varies
slightly as frequency increases over a sevenfold range (Fig. 4).
In the time between these transitions, the blade of the SG
sweeps across the pumping chamber, simultaneously expelling
water through the exhalant channel and drawing water into the
branchial chamber. The SG thus pumps water during both halfcycles of the motor pattern, generating two negative pressure
pulses per cycle (Hughes et al. 1969). The inhalant and
exhalant channels are open simultaneously during the rapid
transitions of the blade tips for approximately 10 % of the cycle
period in each half-cycle. The brief opening of both channels
ensures that the negative pressure in the branchial chamber
does not drop markedly during the ventilatory cycle and hence
minimizes possible back-flow through the system.
The strict phase relationships in the ventilatory motor pattern
may therefore serve two purposes. First, the tight phasing of
the motor pattern at the time of the blade-tip transitions causes
one tip to start its transition immediately after the opposite tip
has reached its maximum levated or depressed position, which
will maximize the expelled volume of fluid and minimize the
time that both tips are in the same (levated or depressed)
position. Second, the maintenance of phase during the
remainder of the motor pattern may serve to produce a smooth,
coordinated movement of the blade as it pumps water through
the system. Any discontinuity in SG movement might disrupt
974
R. A. DICAPRIO, G. JORDAN
AND
T. HAMPTON
the flow of water through the pumping chamber, thereby
decreasing the efficiency of the pump. It is also interesting to
note that ventilation volume and branchial pressure gradient
both increase in exact proportion to the increase in ventilation
frequency, while SG stroke volume remains constant as cycle
frequency increases (Mercier and Wilkens, 1984). In addition,
the efficiency of the ventilatory pump remains constant at
approximately 85 % over a wide range of ventilatory cycle
frequencies (Wilkens et al. 1984). It is possible that the
relationship between these ventilatory parameters and
ventilation frequency may be dependent on constant motor
pattern phase.
We would like to thank Dr Scott Hooper for his extremely
valuable advice and discussions throughout the course of this
work, Dr Joffre Mercier for clarification of the ventilatory
mechanics in Carcinus maenas and Dr Eve Marder for calling
our bluff regarding phase regulation in this system. This work
was supported by a grant from the Whitehall Foundation
(R.A.D.), the Ohio University College of Osteopathic
Medicine and a College of Osteopathic Medicine Summer
Research Fellowship to G.J. and T.H.
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